Research Journal of Applied Sciences, Engineering and Technology 4(17): 3162-3167, 2012
ISSN: 2040-7467
© Maxwell Scientific Organization, 2012
Submitted: April 12, 2012
Accepted: May 14, 2012
Published: September 01, 2012
Enterprise Projects Set Risk Element Transmission Chaotic Genetic Model
Cunbin Li, Peng Li and Gongshu Lu
School of economic and management, North China Electric Power University,
Beijing 102206, China
Abstract: In order to research projects set risk transfer process and improve risk management efficiency in
projects management, combining chaos theory and genetic algorithm, put forward enterprise projects set risk
element transmission chaos genetic model. Using logistic chaos mapping and chebyshev chaos mapping
mixture, constructed a hybrid chaotic mapping system. The steps of adopting hybrid chaos mapping for genetic
operation include projects set initialization, calculation of fitness, selection, crossover and mutation operators,
fitness adjustment and condition judgment. The results showed that the model can simulate enterprise projects
set risk transmission process very well and it also provides the basis for the enterprise managers to make
decisions.
Keywords: Chaos, Genetic Algorithm (GA), projects set, risk element transmission
INTRODUCTION
Enterprise is composed by many projects. The
relationship between these projects is complex and forms
a project set. Through interaction between multiple
projects, it can realize the general objective of the
enterprise. Risk exists in the whole process of project
management. Risk occurring in the certain stage of the
individual project, will produce effects to the project goal.
The impact of the project transmits the risk to the related
projects through the connection of projects. Then the
series of risk transmission process can produce an effect
to the ultimate goal of the enterprise. Consequently, the
risk transmission between projects becomes the focus
research of project risk management.
For multi-projects risk management research, there
are so many literatures. Xie constructed risk decision
model that use in technology innovation project portfolio
choice. This model can use to make risk management
research for technology innovation project portfolio (Xie,
1994). Xian-jin et al. (2007), proposed uncertain
conditions R&D project portfolio selection optimization
model. The model using fuzzy set theory describes fuzzy
uncertainty of R&D project portfolio and sets up R&D
project portfolio risk measure under uncertainty by
bringing fuzzy entropy (Xian-jin et al., 2007). Based on
single project risk and the interaction effects between
projects, Guo et al. (2009) reveals the risk change from
single project to projects portfolio by the risk two
elements (Guo et al., 2009). Chen analysis the problem of
single project risk management model firstly, then put
forward project portfolio risk management model and
projects set risk management model based on enterprise
multi-projects risk management (Chang-fu, 2010).
Eunchang et al. (2009) put forward a kind of risk
management mode of large engineering projects based on
Bayesian incredible network and application in South
Korea shipping industry (Eunchang et al., 2009).
Goncalves et al. (2008) put forward a genetic algorithm
that used to solve the resource constrained multi-project
progress problem (Goncalves et al., 2008). Through the
analogy economic concept, Costa and Barros put forward
an evaluation software project portfolio risk level
technology. The content mainly include that it allow
managers to estimate the probability distribution of the
profit and loss (Helio et al., 2007). The above researches
are considering the risk management from the view of
static and didn display of the dynamic characteristics of
the risk, that is no consider the risk transmission.
To the research of project risk transmission, the
different scholar research direction is difference. The
mainly literatures are shown as follows: (Yuan-Ming and
Dao-zhi, 2008) made a research of construction project
risk transmission. They analyzed construction project
quality risk occurrence and transmit mechanism and
proposed two stages quality control risk transfer model
(Yuan-Ming and Dao-zhi, 2008). On the basis of produce
period risk that affected by it and project environment
factors, Dao-zhi and Yuan-Ming (2008), studied the risk
formation in PERT project single time and all time period
and transmission mechanism (Dao-zhi and Yuan-Ming,
2008). Xiao et al. (2009). considered that product quality
risk has transmission and expand effect from level to level
under the environment of supply chain. They constructed
Corresponding Author: Cunbin Li, School of economic and management, North China Electric Power University, Beijing 102206,
China
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Res. J. App. Sci. Eng. Technol., 4(17): 3162-3167, 2012
the concept of quality supply chain based on quality
function deployment, which used to analysis the technical
characteristic under supply chain environment and
customer demand transfer relationship. Finally, set up the
quality risk transfer model under supply chain
environment (Xiao et al., 2009). Considering the
relationship between construction period and risk of big
integration system project, Xiao-ju and Wang (2004) put
forward a kind of risk transfer algorithm. It can calculate
the system integration project total duration risk (Xiao-ju
and Wang, 2004). Ragnar (1993), devote to the research
of Switzerland energy sector risk transmission influence.
The main content is that CO2 emissions threshold value
change brings the influence of the greenhouse effect risk
(Ragnar, 1993). Bostrom (2003) proposed that: the
development of science and technology has changed the
risk forms of communication. With the Internet and
broadband in the home, the carrier and the medium risk
transfer is changed (Bostrom, 2003). Jürgen (2006) put
forward a different risk spread notion. The risk spread is
not task that spread from the sender information to the
receiver's but a process. In the process, the sender and
receiver made interaction each other in order to achieve
the objective (J gen, 2006). These research results rich
single project risk management theory and provides the
theoretical support for better making project risk
management. And it also laid the solid foundation for
research the risk transfer of multi-projects or projects set.
Based on the analysis of characteristics of the project
set risk element transmission, the study puts forward the
enterprise project set risk element transmission model. In
addition, chaos theory and genetic algorithm are
introduced to study projects set risk element transmission.
The study constructs the projects set risk element
transmission model based on hybrid chaotic genetic
algorithm. It can well solve the enterprise project risk
transfer problem and provide a new method to multiproject risk management.
METHODOLOGY
Enterprise projects set risk element transmission
model: Whether construction enterprise or production
enterprise, it can be regarded as the organic combination
of multiple projects. We called a group projects that in
order to complete the common goal as projects set. Risk
exists in every link of the project implementation.
Because of the transmission of risk and the risk
transmission has "dominoes" effect, if it is not handled
properly or not controlled in risk occurrence link, which
means that a slight change of project risk will bring huge
impact to the ultimate goal of project and projects set.
Risk element is uncertainty factor that can produce
influence to the specific practical consequences at a
specific environment and specific time.
Projects set contain lots of projects and each project
affect by kinds of risk elements. Risk element
transmission in project and between projects, which make
the projects set risk element transmission more
complexity, look be like without rules, desultorily, etc.
Risk element transmits through the time limit chain,
supply chain, cost control chain resources and mixed
chain in projects set. The transmission result has effect on
the goal of projects set. E.g., a project has a time delay in
a stage, which leading to the project period delay or cast
limit time to generate additional costs. Then it leads
project period of delays, cost rise and bring influence to
start or normal operation of the related project. Finally, it
leads to deviate from the project set overall goal, even lost
and so on.
In order to study the complex process, this study
constructs projects set risk element transmission model.
It can be briefly described as follows: First of all, few risk
elements changed in a project, thus caused relevant risk
element change; then integrated these risk elements
change, it can produce effect to the project and make this
project in risk state. Next, the project produces effects to
the related projects, that is, risk element transmission in
projects. Finally, through a series of changes, it has a
great effect on projects set. The model is shown in Fig. 1.
In the process of enterprise projects set risk element
transmission, the transmission from project to another
project is accomplished by the interaction of risk elements
that in projects. The process of interaction between risk
elements is very complex. The change of some risk
elements follow a certain mathematical laws, but in most
cases the risk element change mechanism is quite
complex, not completely obey random distribution.
Therefore, the realization of project objectives based on
the probability model is very different than actual
conditions. In addition, the pattern of risk element
transmission includes chain, hierarchy, network and chaos
etc. The transfer pattern in projects set mix together and
form the complexity transmission process of projects set.
On one hand, project risk element transmission process is
similar to chaotic system, which is not seem rules, but in
some sense, existence rule. On the other hand, risk
element transmission constant changes with time went on,
the risk element that has strong adaptability reserve down
to the next phase of the transfer process. This point is
similar evolution process, therefore, genetic algorithm can
effectively simulation project sets risk element
transmission process. To sum up, the study using chaos
theory and genetic algorithm, studies the process of
projects set risk element transmission.
Enterprise projects set risk element transmission
chaos genetic model: The projects set risk element
transmission has chaos characteristics and evolution
characteristics, this study constructs enterprise projects set
risk element transmission chaos genetic model to study
risk element transmission in enterprise projects set. Chaos
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Res. J. App. Sci. Eng. Technol., 4(17): 3162-3167, 2012
Fig. 1: Projects set risk element transmission model
genetic model steps include: projects set chaos mapping
initialization, calculation of the individual project risk
fitness, selection, crossover and mutation operations, etc.
Specific modeling process is as follows (Yun-Xiao and
Zhou, 2011; Xuefeng et al., 2003).
Hybrid chaos mapping: Projects set risk element
transmission has chaos characteristics, each project
contain few risk elements. Therefore, adopt chaotic
sequence to initialize the risk state of projects set. The risk
element of project has sensitivity of initial state and the
uniformity of changes and so on. So, a single chaos
mapping can't meet its requirements. Using Logistic
mapping and Chebyshev mapping mixed chaos mapping
is constructed.
The hybrid mapping makes the connection variables
of Chebyshev map and Logistic map. The seed values of
offspring chaotic sequence use the father generation chaos
mapping result. It improves the uniformity of the
generation chaotic sequence and formats a unified output
sequence. The specific expression is shown as following:
know that the value of k and : is 4, respectively. The
hybrid chaotic sequence gets to chaotic state. The system
first generated yn through the Chebyshev map chaos
generator, then based on Logistic chaos mapping
generation intermediate state chaotic sequence, finally, it
obtains the final chaotic sequence through amendment.
Through the hybrid chaotic system to produce a chaotic
sequence, it has the initial value sensitivity, ergodicity and
uniformity, as shown in Fig. 2 shows.
Projects set risk element chaos initialization: Firstly,
generate a chaotic sequence by hybrid chaos mapping to
initialize projects set. Then, make the initial project set
chaotic sequence as the initial value and generate a new
chaotic sequence by hybrid chaotic system. Finally, use
the new chaotic sequence as the individual project risk
element value. The specific process is as follows:
Suppose: Projects set contain N projects. The number of
influence risk of each project is m. Then the projects set
show as following:
y0 = x0
P {P1, P2, ......, PN}
P {Pi1, Pi2, ......, Pim}
y n +1 = cos( k arccos y n )
tep = µx n (1 − x n ) + y n +1
(1)
x n +1 = mod(temp,1)
x0, y0 is the initial value of hybrid chaos. :, k is the control
variable of the hybrid chaotic sequence. According to the
characters of Logistic map and Chebyshev map, we can
(2)
P = indicate the initial projects set
Pi = indicate the individual of projects set
Pij = stand for the risk element of individual of projects
set
The maximum value of influence by risk element is
L and then the initial of projects set show as follow:
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Res. J. App. Sci. Eng. Technol., 4(17): 3162-3167, 2012
hy brid c haot ic mapping digram
1
0. 9
v alue of hy birid c haos s equence
0. 8
0. 7
0. 6
0. 5
0. 4
0. 3
0. 2
0. 1
0
0
100
200
300
400
500
t
Fig. 2: Hybrid chaotic system simulation diagram sequence
P1 = L×{x11, x12, ..., x1j, ..., x1m}
P2 = L×{x21, x22, ..., x2j, ..., x2m}
...
700
800
900
1000
where, x0, x1, x2, ......, xs is a chaotic sequence generate by
the initial value x0 .
...
Pi = L×{xi1, xi2, ..., xij, ..., xim}
(3)
where, x11, x21,..., xi1,..., xN1 is the chaotic sequence
generate by hybrid chaos system.
Genetic operations based on hybrid chaos: Apply
hybrid chaos sequence in selection, crossover and
mutation operation, which can improve randomness and
uniformity in projects set risk element transfer process by
using the features of hybrid chaotic sequence.
Chaotic selection operation: Generate a chaotic
sequence by using hybrid chaotic system. {x0, x1, x2,.....
x k}
where, k is the number of joining selection operation.
Then, the sequence number of selection is decision by the
formula shown as follow:
{([k × x ],[k × x ]), ([k × x ],[k × x ]),....., ([k × x ],[k × x ])} (4)
0
600
1
2
3
2k −2
2 k −1
Chaotic mutation operation: The mutation operation
also uses the hybrid chaotic sequence to choose the risk
element mutation serial number j. The serial number j is
decision by the formula (6):
j = [m xi]
where, xi is the hybrid chaotic sequence.
Adaptive crossover probability and mutation
probability: Crossover probability and mutation
probability play an important role in chaos genetic
models. Fixed probability can't real-time reflect the
dynamic situation of projects set, so the study puts
forward a adaptive crossover probability and mutation
probability (Gharooni-farda et al., 2010; Wu, 201.0)
Adaptive crossover probability: According to the
general crossover probability in between 0.4 and 0.99, we
make the change as following:
f max − f ave
⎧
, f ave ≤ f max
⎪ Pcross = 0.4 + 0.6 × K1
f max
⎨
⎪P
⎩ cross = 0.4 + 0.6 × k1, f ave > f max
where, x0, x1, x2, x3,......, x2k!1 indicate the hybrid chaotic
sequence generate by the initial value x0. [k×x0] indicate
get the round number.
After the process, we get k pairs number of project.
Chaotic crossover operation: The number of risk
element is m. So, the position of attention crossover
operation risk element is decision by the formula (5):
{[m×x0], [m×x1], [m×x2], ......, [m×xk]}
(6)
(7)
Adaptive mutation probability:
(5)
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f max − f
⎧
, f > f ave
⎪ Pmutation = k 3
f max − f ave
⎨
⎪P
f ≤ f ave
⎩ mitation = k 4 ,
(8)
Res. J. App. Sci. Eng. Technol., 4(17): 3162-3167, 2012
Construct fitness
function
N
Projects set
initialization
Selection
Hybrid chaotic
sequence
Crossover
Judgment
Y
Put out
final result
Mutation
Fig. 3: Flow chart of enterprise projects set risk element transmission chaos genetic model
0.75
where,
0.70
=
=
=
=
=
=
The crossover probability
The mutation probability
The biggest value of fitness
The average value of fitness
The individual value of fitness
Constant coefficient
Value of project risk
Pcross
Pmutation
fmax
fave
f
k1 , k2 , k3 , k4
0.60
0.55
0.50
0.45
0.40
0.35
Value of project risk
Basic process of enterprise projects set risk element
transmission chaos genetic model: The projects set risk
element transmission chaos genetic model Flow chart is
shown in Fig. 3.
Model simulation and analysis:
Basic assumptions: A projects set contains 50 projects.
These projects connect together through capital chain,
period chain, resources supply chain and cost chain and
form a complex nonlinear system. There are many kinds
of risk elements in project environment. For example,
policies and regulations and natural conditions, economic
conditions and technological conditions, human factors
and so on. Those risk elements have effect on the project
and the connection of projects. A slight change of point,
that will give related node and project bring certain effect,
finally bring the influence to the projects set goal. In order
to the simulation of convenient, this study takes 8 risk
elements for simulation. In order to keep the initial model
operation, set the initial crossover probability was 0.85,
the variation probability for 0.07.
0.65
0
5
10
15
20
25
K
30
35
40
45
50
0
5
10
15
20
25
K
30
35
40
45
50
0.80
0.75
0.70
0.65
0.60
0.55
0.50
0.45
0.40
0.35
state, risk value difference is bigger from project to
project among projects set, besides risk value of many
projects is greater than the threshold level (0.6); After
fifty generation of chaos genetic risk transmission, risk
RESULTS OF THE SIMULATION EXPERIMENT
Fig. 4: Projects set risk element transmission simulation
the red line is the normal value of project risk
Figure 4 is the simulation figure of 50 projects and 8
risk elements. The time of iteration is 50. The projects set
eventually risk probability distribution shows in Fig. 4.
We can see that, after 50 times between projects risk
element transmission, the project risk probability have a
greatly change than the initial state. The simulation results
show that the risk status value of projects set gradually
change from the initial uneven to uniform. In the initial
state of projects set moderate and most projects' risk value
is under normal level, only a few of projects are at risk
state. According to the distribution of project risk value at
the end of simulation, we can be used for analyzing the
impact change of the whole project through risk element
transmission. Then monitor the risk value project and
prevent the occurrence of a risk, so as to achieve the
ultimate goal of the project set.
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Res. J. App. Sci. Eng. Technol., 4(17): 3162-3167, 2012
Application of enterprise projects set risk element
transmission chaotic genetic model: Because of the
complexity of the projects set connection, the traditional
analytical method to solve the projects set risk element
transfer problems has failed to meet the needs of practical
application. Therefore, intelligent simulation method will
become the first choice tools of projects set risk element
transfer. The change of a project node, will lead to the
corresponding node change. That is the projects set risk
element transmission has initial value sensitivity and
randomness. Above analysis show that projects set risk
element transmission is a complex system and chaotic
systems. Therefore, we can use the chaos mapping to
simulate the evolution process of enterprise projects set
risk element transmission. Random change of some nodes
in projects set, can simulate through the chaos genetic
model before enterprise decision, we can forecast the
projects set risk and analyze some factors change to
variations of projects set risks.
CONCLUSION
Along with the enterprise scale and business
expansion, the links between enterprise projects become
more closely. The effects of projects set risk element
transmission is expanding at the same time. Based on the
analysis of projects set risk element, the study proposes
the model of enterprise projects risk element transmission
and construct the chaos genetic model of enterprise
projects set risk element. The chaos genetic model of
enterprise projects set risk element, adopt chaos theory
and genetic algorithm and apply hybrid chaos mapping
system to build enterprise projects set risk element initial
transmission state. Then, use the chaotic selection,
crossover and mutation operation for genetic operation,
which is the process of projects set risk element
transmission. Utilizing the model can help the manger to
make decision. When the decision maker faces the change
of risk element, the model could help to forecast the
projects set risk state change. According to the forecast
results, the manager can make relevant decision and avoid
high-risk decisions.
ACKNOWLEDGMENT
This study is supported by National Natural Science
Funds of China (No. 71071054) and 211 Project of North
China Electric Power University.
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